SURFACE AREA AND VOLUME OF A CUBE EXAMPLES

Solved Examples

Example 1 :

The volume of the cube is 125 dm³. Find its side.

Solution :

Volume of cube  =  125 dm³

a³  =  125

a³  =  5³

a  =  5 dm

So, side length of cube is 5 dm.

Example 2 :

A container is in the shape of a cube of side 20 cm. How much sugar can it hold?

Solution :

In order to find the quantity of sugar that the container can hold, we have to find the volume of container.

Side length of cubical container  =  20 cm

Volume of container  =  a³

  =  (20)³

  =  8000 cm³

Example 3 :

A cubical tank can hold 64,000 litres of water. Find the length of the side of the tank.

Solution :

Let a be the side of the cubical tank. Volume of the tank is 27,000 litres. So,

V  =  a³  =  (27000/1000)

a³  =  27

a  =  ∛27

a  =  3 m

Example 4 :

Three metallic cubes of side 3 cm, 4 cm and 5 cm respectively are melted and are recast into a single cube. Find the total surface area of the new cube.

Solution :

Side length of 1^st cube  =  3 cm

Side length of 2^nd cube  =  4 cm

Side length of 3^rd cube  =  5 cm

Volume of 1^st, 2^nd and 3^rd cube  =  3³ + 4³ + 5³

  =  27 + 64 + 125

  =  216

a³  =  216

a³  =  6³

a  =  6 cm

Total surface area of new cube  =  6a²

  =  6(6)²

  =  6(36)

  =  216 cm²

So, total surface area of new cube 216 cm²

Example 5 :

Find the L.S.A, T.S.A and volume of a cube of side 5 cm.

Solution :

Lateral surface area (L.S.A)  =  4a²

  =  4(52 ) = 100 sq. cm

Total surface area (T.S.A)  = 6a²

=  6 (5² )

=  150 sq. cm

Volume of cube  =  a³

  =  5³

  =  125 cm³

Example 6 :

Find the length of the side of a cube whose total surface area is 216 square cm.

Solution :

Let a be the side of the cube.

Given that T.S.A = 216 sq. cm

6a²  =  216 

a²  =  216/6 

a²  =  36

a  =  √36

a  =  6 cm

Example 7 :

A cube has a total surface area of 384 sq. cm. Find its volume.

Solution  :

Let a be the side of the cube. Given that T.S.A = 384 sq. cm

6a² = 384

a²  =  384/6

a²  =  64

a  =  √64  =  8 cm

So, volume is

=  a³

=  8³

=  512 cm³

Example 8 :

If the lateral surface area of a cube is 900 cm², find the length of its side.

Solution :

Lateral surface area of cube  =  4a²

4a²  =  900

a²  =  900/4

a²  =  225

a  =  √225

a  =  15 cm

So, the side of cube is 15 cm. 

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.